The value of the det is (A + B + C)^3
I found it's value with the tri method.
We have to prove that , The given is A , B, C > 0 so we can say their sum is also > 0 (A+B+C)^3 > 0
But expanding this A + B +c will take up to decade .
here is a method to show this is true
What's the method ?
lets say ABC are all approaching the same number,
now u were to begin varying B and C,
we can rewrite B and C as A-k
and lets Say we always make sure that A is always the biggest number or equal
So we will make assumption that A > b,c and b, c are approaching A
I have problem with electricity , I will re-log soon , sorry.
you can begin cancelling terms now
oh apparently there is a neat solution to this
for positive numbers
heres a proof for the binomial case, maybe u can spend some time to prove it for the trinomial
This is the arthmetic , geometric sequence inequality right ?
The Arithmetic mean is always greater than the geometric mean
But can you write the proof of this inequality ?
id have to work it out too,
Are you good with maxima and minima applications and complex number ?
sure : )
I will open a new question